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 May 14 accepted If the sum of two independent random variables is in $L^2$, is it true that both of them are in $L^1$? May 13 revised If the sum of two independent random variables is in $L^2$, is it true that both of them are in $L^1$? added 148 characters in body May 13 comment If the sum of two independent random variables is in $L^2$, is it true that both of them are in $L^1$? @Batman That's why proving $X$ and $Y$ are in $L^1$ should be an easier task, isn't it? May 13 comment If the sum of two independent random variables is in $L^2$, is it true that both of them are in $L^1$? Can you give an example s.t. $\mathbb E(X+Y)^2 < \infty$ but $\mathbb E X = \infty$ and $\mathbb E Y = \infty$? May 12 comment 1D biased random walk - is the event of infinte many returns a tail event? You should check Hewitt–Savage zero–one law - en.wikipedia.org/wiki/… May 12 asked If the sum of two independent random variables is in $L^2$, is it true that both of them are in $L^1$? May 7 comment hat problem and probability If the colors are assigned at equal probability and independently, you will not be able do better than 1/2. May 5 revised Simple probability problem? typos May 4 answered Simple probability problem? Mar 10 awarded Popular Question Mar 2 awarded Notable Question Dec 8 awarded Popular Question Nov 17 comment The limit of integer valued random variables must be integer valued? OK. BTW, does my example shows that the portmanteau theorem works only for random variables on $\mathbb R$? Nov 17 accepted The limit of integer valued random variables must be integer valued? Nov 17 comment The limit of integer valued random variables must be integer valued? It's not clear whether the author meant to define $D_n$ and $D$ in $\mathbb R$ or compactification of $\mathbb R$. That's a question that comes to me again and again -- When the author says "random variables", does he/she allow them to take $\infty$ as value or not? Nov 17 comment The limit of integer valued random variables must be integer valued? Thanks. I'm actually aware of this theorem and it is how I thought I had proved it. But when I came up with the "counter example" that I got confused again. Can we say that $\infty \in \mathbb Z$? Nov 17 asked The limit of integer valued random variables must be integer valued? Nov 6 awarded Popular Question Oct 24 awarded Popular Question Sep 1 awarded Yearling